Author(s): Betriz Negreiros; Sebastian Schwindt; Stefan Haun; Silke Wieprecht
Keywords: Fuzzy logic; Map comparison; Hydro-morphodynamics; Numerical modelling; Kappa statistics
Abstract: The validation of the accuracy of a numerical model counts to the numerous challenges in modeling hydro-morphodynamics. Many state-of-the-art approaches compare pixel-by-pixel topographic change using statistics such as Pearson’s correlation coefficient. However, these statistics may not enable to differentiate between fairly well-performing models and complete non-sense models. This study employs spatially explicit map comparison techniques based on fuzzy sets to evaluate the efficiency of two-dimensional numerical hydro-morphodynamic models. We test a recently developed fuzzy numerical and a fuzzy kappa map comparison method for comparing observed topographic change with numerically modeled topographic change of a physical laboratory model. Fuzzy numerical map comparison introduces one level of fuzziness to compensate for spatial offset between modeled and observed values. Fuzzy kappa map comparison adds another level of fuzziness to account for similarities between categories. To this end, we categorize topographic change into categories of erosion and deposition. The results suggest that fuzzy kappa map comparison provides a suitable statement of the goodness of a numerical model, while fuzzy numerical map comparison shows limitations for expressing subjectively perceived correlation between modeled and observed topographic change. For instance, fuzzy numerical-based similarity coefficients are considerably high, even for a quasi-random non-representative model. We conclude that fuzzy map comparisons represent a powerful tool for the validation of hydro-morphodynamic numerical models.